**A Refined Mean Field Approximation**

Mean field approximation is a widely used technique to study stochastic systems composed of many interacting objects with applications from theoretical physics to biological models and artificial intelligence. In computer science, mean field approximation has been successfully used to analyze the performance of many distributed algorithms, including allocation strategies in server farms, caching algorithms and wireless protocols. The fundamental idea of mean field approximation is to study the limiting behavior of the system as the number of interacting objects goes to infinity. This limiting system is often much easier to study. In this talk, I will introduce the key concepts behind mean field approximation, by giving some examples of where it can be applied. I will review some of the classical models and their convergence properties. I will try to answer a very natural question: how large should the system be for mean-field to apply? This leads to a follow-up question: can we improve this approximation?